The Hall effect is widely used in devices intended for measuring, controlling and regulating purposes. For example, in combination with a voltage amplifier, a Hall effect element may be used as a stable signal generator or as a switch or boundary value indicator which functions without physical contact.
The theory of operation of Hall effect devices is well known. A block or sheet of suitable material having orthogonal axes X, Y and Z is fitted with a pair of input electrodes such that a current flows along the X axis and, if a magnetic field is passed through the material generally parallel with the Y axis, then a Hall voltage will be produced across the material in the direction of the Z axis. A pair of output electrodes may be connected to the material such that the Hall voltage can be applied to an output circuit.
Materials suitable for Hall effect devices generally exhibit large increases in resistance with increasing temperature. Thus, a fixed voltage applied to a Hall or other similar element results in a current therethrough which decreases rapidly with increasing temperature. As a result of the decreasing current the output voltage of the Hall element decreases. This large negative temperature coefficient is manifested as a reduction in sensitivity as temperature increases. In many applications a large variation in sensitivity cannot be tolerated or is at least undesirable. In such applications it is necessary to provide means for compensating for the temperature dependence.
A variety of circuits and apparatus have been devised for compensating for the temperature dependent characteristics of a Hall element. For example, British
Pat. No. 1,247,955 discloses Hall effect apparatus in which an attempt is made to provide temperature independent sensitivity, in part by maintaining a constant current through a Hall element by connecting large value resistors in series therewith. The apparatus also includes an output circuit in which the internal resistance of the Hall element forms part of a feedback network for a differential amplifier.
A more practical and widely accepted method for temperature compensation of Hall effect circuits is shown in U.S. Pat. No. 4,521,727 to Atherton, et al. Through use of compensation threshold voltage directly proportional to the current flowing through the Hall element, a magnetic switch point is achieved which is dependent only on the Hall scattering coefficient which has a temperature coefficient of about +700ppm/.degree. C. Key to this method, however, is the use of a resistance element which is temperature independent. Unfortunately, temperature independent resistors such as CrSi thin film resistors must be formed during the circuit fabrication process by process steps not ordinarily employed in manufacturing the Hall element device and associated circuitry. Thus the cost of making such temperature compensated circuits is greatly increased because of the time and expense involved in making the required temperature independent resistor.
The sensitivity of a Hall element can be expressed as: ##EQU1## wherein: B.sub.Z =Magnetic induction perpendicular to plane of the sensor
q=Charge on the electron PA1 N.sub.D =N-type carrier density in the Hall element PA1 t=Thickness of the Hall element PA1 V.sub.H =Hall voltage PA1 I.sub.Y =Current in the Hall element PA1 G.sub.T =Hall element geometry factor ##EQU2## PA1 R.sub.H =Impedance of Hall element. PA1 L=Length PA1 W.times.Width
The current in the Hall element can be expressed as ##EQU3## wherein: V.sub.a =Voltage across Hall element
Impedance of the Hall element may be expressed as: ##EQU4## wherein: .rho.=Resistivity
Since: ##EQU5##
Hall sensitivity may be expressed as: ##EQU6## Thus Hall sensitivity is directly proportional to the bias voltage applied to the Hall element and proportional to Hall mobility. Since drift mobility is directly related to Hall mobility, a control element responsive to drift mobility changes with temperature can be used to accurately determine changes in sensitivity under conditions where V.sub.a is held constant.